Re: Reasons why i believe that Jiraiya would beat Itachi Uchiha in a battle:
I also think that Jiraiya would win this one.
Not only that, but he can summon Fukasaku and Shima, which are above Jonin level summons themselves. Both of whom can use sage jutsu. In order to use Sage Mode, you have to have a giant amount of chakra. So we are going to assume that Jiraiya has a ton of stamina because of it.
Itachi has stamina. More than Kakashi, but that isn't saying much. Jiraiya could battle longer and use more taxing jutsu.
If Jiraiya summoned Gamaken, or Gamabunta, or Gamahiro, or at least any two of them, Susanoo could possibly be held down. The Baku that Danzo summoned proved that Susanoo is affected by things with mass because it had to hold itself down to avoid being sucked in. So if they create an opening, Jiraiya could rush in.
Frog song is a genjutsu, and genjutsu is the Sharingans specialty. This is true. However, they are not experts at Genjutsus that attack using sound. Also, it is kinda weird how they materialized those stone swords when Jiraiya, Shima, and Fukasaku pierced Pains bodies, but it could just be part of the illusion.
I do believe that Tsukiyomi would fall before Sage Mode. Look at when Itachi used it on Sasuke. Yes, Itachi was holding back, but there is nothing stating that it wasn't a regular Tsukiyomi. Itachi may have just expected Sasuke to break out of it. Sasuke broke out of it by using the cursed seal to alter his chakra. When Sasuke used it against Killer Bee, Killer Bee used tailed beast chakra to break out of it.
Jiraiya has natural energy. Nuff said on that.
Amaterasu would be tough. It has not been confirmed if Jiraiya has the sage mode speed to outrun it. I guess if he summons some frogs to attack Itachi while he runs around that would disrupt Itachi's field of vision, then Jiraiya could use the needle technique to pierce Itachi, because apparently it is a fast attack.
Itachi CANNOT see Sage Chakra, which would mean frog katas can hit him. If Itachi could see Sage Chakra, then he would be blind using the Sharingan cause all the Sage Chakra would be in his face.
And of COURSE Itachi would say that. They all hype themselves up in Naruto.
Zabuza: There are eight vital spots, which one of yours should I target?
Kisame: If you can pry it from my body, that is.
They all say that kind of stuff.